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ERIC Number: ED368789
Record Type: RIE
Publication Date: 1994-Apr
Reference Count: N/A
A Comparison of the Mallows' C subscript p and Principal Component Criteria for Best Model Selection in Multiple Regression.
Schumacker, Randall E.
A population data set was randomly generated from which a random sample was drawn. This sample was randomly divided into two data sets, one of which was used to generate parameter estimates, which were then used in the second data set for cross-validation purposes. The best variable subset models were compared between the two data sets on the R-squared and the Mallows' C(p) criteria for best model selection. The cross-validation method postulated a correlated predictor set. The parameter estimates, standard errors, and t values of the best variable subset models were then compared between the multiple regression approach with correlated predictors and the principal components method that creates orthogonal predictor variables. The Mallows' C(p) values were inflated and did not always indicate the best variable subset model upon cross validation. The R-squared values are the same regardless of correlated or orthogonal predictors; therefore, parameter estimates and standard errors in a principal components analysis should be investigated. This is especially the case in the presence of multicolinearity in the best variable subset model predictor set. The use of PROC IM1 procedures for cross validation is discussed. Ten tables and one figure illustrate the discussion. An appendix presents analysis programs. (Contains 23 references.) (Author/SLD)
Publication Type: Reports - Evaluative; Speeches/Meeting Papers
Education Level: N/A
Authoring Institution: N/A
Identifiers: Cross Validation; Mallows C(p) Criterion; Multicollinearity; Principal Components Analysis; Statistical Package for the Social Sciences; Statistical Packages; Subset Analysis
Note: Paper presented at the Annual Meeting of the American Educational Research Association (New Orleans, LA, April 4-8, 1994).